Equation 677 Database

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Magma b7aaadbf14fa…

magma b7aaadbf14fa
Size
381
Isomorphism class hash
b7aaadbf14fa84cddcd47fb7ff5ec194f4fb38ebac4d395fc489278ce9903a2d
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:45:38
Display reorder
380,86,91,280,106,95,100,191,195,200,175,180,185,170,160,165,296,0,1,120,110,115,130,125,286,56,51,270,45,36,40,227,232,221,210,215,206,276,65,60,75,80,70,145,151,156,136,290,141,15,20,10,265,31,26,316,317,315,313,314,312,255,250,260,235,242,245,360,366,340,350,330,335,356,346,372,375,85,90,281,105,96,101,190,196,201,176,181,186,171,162,167,295,2,3,121,111,116,131,126,285,55,50,271,47,35,42,228,233,220,211,216,205,275,67,61,76,81,71,146,150,157,135,291,140,17,24,13,267,32,27,324,325,323,327,328,326,257,252,262,237,240,247,361,365,341,351,332,336,355,345,373,376,87,92,282,107,97,102,193,198,203,178,183,188,172,163,168,297,4,5,123,112,118,132,127,287,57,52,272,48,37,43,226,231,223,213,218,208,277,68,62,78,83,73,148,152,158,137,292,142,18,21,12,268,33,28,310,311,309,307,308,306,258,253,263,238,243,248,362,367,342,352,333,337,357,347,371,378,89,94,284,109,99,104,194,199,204,179,184,189,174,161,166,299,8,9,124,114,119,134,129,289,59,54,274,49,39,44,229,234,224,214,219,209,279,69,64,79,84,74,147,154,155,139,294,144,19,23,14,269,34,29,301,300,302,303,304,305,259,254,264,239,244,249,364,369,344,354,334,339,359,349,374,379,88,93,283,108,98,103,192,197,202,177,182,187,173,164,169,298,6,7,122,113,117,133,128,288,58,53,273,46,38,41,225,230,222,212,217,207,278,66,63,77,82,72,149,153,159,138,293,143,16,22,11,266,30,25,321,322,320,319,329,318,256,251,261,236,241,246,363,368,343,353,331,338,358,348,370,377 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, M = {72} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:45:39 · history